Question

1. Consider the joint probability distribution of window orders for a company in 2017 given the table below. The measurements for the width and height of double hung windows are where X denotes the width and Y de height. Xand Y are dependent. notes the Y-width 32" 0.05 0.15 0.10 0.30 44" 0.05 0.05 0.15 48" 44" 48* 0.10 0.05 a) What is the probability that a customer ordered a square window (width height)? (10 pts) What is the probability that a customer ordered a window that has an area of at least 1936 square inches? (10 pts) b) c) Find the covariance for X and Y. (10 pts) d) is there a strong, moderated or weak linear relationship between X and Y? Explain your answer. (10 pts)

Answer 1

(a)

P (customer order square window) = P (X= 44, Y = 44) + P (X = 48, Y= 48) = 0.05+ 0.10 = 0.15.

(b)

P (XY >= 1936) = P (X = 44, Y = 44) + P( X = 44, Y = 48) + P ( X= 48, Y=44) + P (X=48, Y=48) +P (X = 52, Y = 44) + P (X = 52, Y = 48)

= 0.05 + 0.05 + 0.15 + 0.10 + 0.30 + 0.05

= 0.70

(C)

E (X) = 44× 0.15 + 48 × 0.40 + 52 × 0.45

= 6.6 + 19.2 + 23.4

=49.2

E (Y) = 32× 0.30 + 44 × 0.50 + 48 × 0.20

= 9.6 + 22.0 + 9.6

= 41.2

E (XY) = 2028

Cov (X, Y) = E (XY) - E (X) E (Y) = 2028 - 49.2 × 41.2

= 0.96

(d) r = 0.05412

There is week Correlation.

Alignment matting Table styles Number F18 32 48 p(x) x*p(x) x^2*p(x) x*y"p(x,y) 4 70.4 96.8 105.6 0.05 230.4 316.8 230.4 0.15 166.4686.4 124.8 272.8 0.05 0.05 0.15 6.6 290.4 48 0.15 0.1 0.4 19.2 921.6 8 977.6 0.1 0.3 9.6 0.3 0.5 52 0.050.4523.4 1216.8 ply) y"ply) yA2*p(y) 307.2 968 460.8 1736 x*y*p(x,y 467.2 1100 460.82028 1 49.2 2428.8 2028 41.2 10 0.2 9.6 12 13 14 15 16 cov(x,y)- correlatior 0.05412 0.96 18 Ankey Sheet2 Sheet3 ms N Sheet Sheet! Sheets2

N M pause ↑shift alt gr ctri OCTOBER 2017 02 Wx40 DAY 275-090 MONDAY Cov(x, y wx 40 DAY 276-D89 TUESDAY C6) 2017 NOVEMBER 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30